When creating and modifying External Content Types in SharePoint, you may see the error Access denied by Business Data Connectivity.
This usually means that you need to give permissions to specific users and groups for that External Content Type. To set the permissions, here's the procedure:
~ Open SharePoint 2010 Central Administration on the server that holds the web service and click on Manage service applications.
~ Click on Business Data Connectivity Service.
~ Select the External Content Type and click Set Object Permissions.
~ Then in the resulting Set Object Permissions dialog box, add yourself and/or someone else and/or a group and/or All Authenticated Users. Assign the necessary permissions that are required for the users and groups.